Size exclusion chromatography with superficially porous particles
超微孔颗粒尺寸排除色谱法

Mark R. Schure $^{a, *}$ , Robert E. Moran $^{b}$ a Theoretical Separation Science Laboratory, Kroungold Analytical, Inc., 1299 Butler Pike, Blue Bell, PA, 19422 USA $^{b}$ Advanced Materials Technology, Inc., 3521 Silverside Road, Suite 1-K, Quillen Building, Wilmington, DE, 19810, USA
$^{b}$ Advanced Materials Technology, Inc.，3521 Silverside Road, Suite 1-K, Quillen Building, Wilmington, DE, 19810, USA

A R T IC LE IN F O
在 F O

Article history: 文章历史：

Received 24 September 2016
2016 年 9 月 24 日收到
Received in revised form 7 November 2016
2016 年 11 月 7 日收到修订稿
Accepted 9 December 2016 2016 年 12 月 9 日接受
Available online 9 December 2016
2016 年 12 月 9 日在线提供

Keywords: 关键词：

Size-exclusion chromatography
尺寸排阻色谱法
Core-shell particles 核壳粒子
Superficially porous particles
表面多孔的颗粒
Efficiency 效率
Pore diffusion 孔隙扩散
Peak capacity 峰值容量

Abstract 摘要

A comparison is made using size-exclusion chromatography (SEC) of synthetic polymers between fully porous particles (FPPs) and superficially porous particles (SPPs) with similar particle diameters, pore sizes and equal flow rates. Polystyrene molecular weight standards with a mobile phase of tetrahydrofuran are utilized for all measurements conducted with standard HPLC equipment.
本研究使用尺寸排阻色谱法（SEC）对具有相似颗粒直径、孔径和相同流速的全多孔颗粒（FPPs）和超多孔颗粒（SPPs）的合成聚合物进行了比较。所有测量均采用标准 HPLC 设备，以四氢呋喃为流动相的聚苯乙烯分子量标准。

Although it is traditionally thought that larger pore volume is thermodynamically advantageous in SEC for better separations, SPPs have kinetic advantages and these will be shown to compensate for the loss in pore volume compared to FPPs. The comparison metrics include the elution range (smaller with SPPs), the plate count (larger for SPPs), the rate production of theoretical plates (larger for SPPs) and the specific resolution (larger with FPPs). Advantages to using SPPs for SEC are discussed such that similar separations can be conducted faster using SPPs.
尽管传统观点认为，在 SEC 中，较大的孔隙率在热力学上有利于实现更好的分离，但 SPPs 具有动力学优势，与 FPPs 相比，这些优势将被证明可以弥补孔隙率的损失。比较指标包括洗脱范围（SPPs 较小）、板数（SPPs 较多）、理论板速率（SPPs 较多）和特定分辨率（FPPs 较多）。讨论了使用 SPPs 进行 SEC 的优势，即使用 SPPs 可以更快地进行类似的分离。

SEC using SPPs offers similar peak capacities to that using FPPs but with faster operation. This also suggests that SEC conducted in the second dimension of a two-dimensional liquid chromatograph may benefit with reduced run time and with equivalently reduced peak width making SPPs advantageous for sampling the first dimension by the second dimension separator. Additional advantages are discussed for biomolecules along with a discussion of optimization criteria for size-based separations.
使用 SPP 的 SEC 与使用 FPP 的 SEC 具有相似的峰容量，但运行速度更快。这也表明，在二维液相色谱仪的二维中进行 SEC 可缩短运行时间并相应减少峰宽，从而使 SPPs 在通过二维分离器对一维进行采样时更具优势。此外，还讨论了生物大分子的其他优势，以及基于粒度分离的优化标准。

1. Introduction 1.导言

Size exclusion chromatography (SEC) is a form of chromatography that separates molecules by size. It is also known as gel-filtration chromatography (GFC) and gel permeation chromatography (GPC) which often refers to SEC with organic solvents. The primary applications of this technique are polymer and medium to large biomolecule separations. The performance characteristics of SEC are not on the scale of the efficiencies typical of columns used for reversed-phase or normal-phase separations. However, SEC continues to be highly utilized for separations where fractionation can be accomplished based on molecular size.
尺寸排阻色谱法（SEC）是一种按尺寸分离分子的色谱法。它也被称为凝胶过滤色谱法（GFC）和凝胶渗透色谱法（GPC），通常指使用有机溶剂的 SEC。这种技术的主要应用领域是聚合物和大中型生物大分子分离。SEC 的性能特点与反相或正相分离柱的典型效率不同。不过，在可以根据分子大小进行分馏的分离过程中，SEC 仍有很高的利用率。

The first SEC columns were made of starch [1,2], however, dextran gels were soon developed for biochemical applications [3]. After this initial introduction, cross-linked polystyrene was introduced [4] as a material useful for fractionating industrial polymers. Silica is also often utilized as a porous medium and complements other media, especially when small particles are used to minimize zone broadening and provide a stable mechanical particle for use
最早的 SEC 色谱柱是由淀粉制成的[1,2]，但很快就开发出了用于生化应用的葡聚糖凝胶[3]。之后，交联聚苯乙烯作为一种可用于分馏工业聚合物的材料问世[4]。二氧化硅也经常被用作多孔介质，与其他介质相辅相成，特别是当使用小颗粒时，可最大限度地减少区域扩展，并提供稳定的机械颗粒，以便使用

at higher pressures [5,6]. In most cases, particles are used for SEC although polymer monoliths have been reported that can function in the size-exclusion mode [7].
5,6] 。大多数情况下，SEC 使用颗粒，但也有报道称聚合物单片可在尺寸排除模式下发挥作用 [7]。

In all cases where particles are used for SEC, the particle is made of organic or inorganic materials and is a fully porous particle (FPP) morphology. Superficially porous particles (SPPs) [8-13], also known as core-shell particles, offer the performance of a smaller diameter particle, for example a sub

2 - μ m

diameter particle, with the smaller pressure drop of a standard-sized particle, for example

a \geq 2.7 μ m

particle. The SPP morphology has become a serious choice for high performance chromatographic media. In the early development of SPP materials, specifically from 1978, it was written by one of the developers of the SPP technology [14]: “However, it is anticipated that, while wide-linear calibrations should result, resolution of polymers with these particular particles would be relatively poor because of their low specific porosity.”
在所有将颗粒用于 SEC 的情况中，颗粒都是由有机或无机材料制成，并具有全多孔颗粒 (FPP) 形态。表面多孔颗粒 (SPP)[8-13]，也称为核壳颗粒，具有较小直径颗粒（例如直径小于

2 - μ m

的颗粒）的性能，同时具有标准尺寸颗粒（例如

a \geq 2.7 μ m

的颗粒）的较小压降。SPP 形态已成为高性能色谱介质的重要选择。在 SPP 材料的早期开发中，特别是从 1978 年开始，SPP 技术的开发者之一写道[14]："不过，预计虽然会产生宽线性定标，但由于这些特定颗粒的比孔隙率较低，因此聚合物的分辨率会相对较差"。

The assumption inherent in this quote is that it is necessary to have as much pore volume as possible to get maximum performance from the SEC technique. This assumption is partly driven by the low peak capacity inherent in the SEC technique where getting a 10 peak separation would be considered a large number of peaks [15-17]. This is in contrast to getting peak counts greater than 60 which is not uncommon [18] using the partition
这句话的内在假设是，有必要拥有尽可能多的孔容积，以获得 SEC 技术的最大性能。这一假设的部分原因是 SEC 技术的固有峰容量较低，能分离出 10 个峰值就已经算是大量峰值了 [15-17]。与此形成鲜明对比的是，使用分区技术获得大于 60 个峰值的情况并不少见[18]。
and adsorptive retention mechanisms inherent in reversed-phase liquid chromatography [19].
和反相液相色谱固有的吸附保留机制 [19]。

Recent theoretical work [20,21] has concluded that reducing the pore volume by using a SPP for SEC would not be especially deleterious for large-sized solutes with slow diffusional characteristics. This work highlighted that the loss of pore volume can be compensated by shortening the diffusion length of the solutes inside the pore and theoretical elution curves which showed this effect were given in detail [20,21]. These results suggest that SPPs could be used successfully for SEC.
最近的理论研究[20,21]得出结论，在 SEC 中使用 SPP 减少孔隙体积对具有缓慢扩散特性的大体积溶质不会造成特别严重的影响。这项工作强调，孔体积的损失可以通过缩短孔内溶质的扩散长度来补偿，并详细给出了显示这种效果的理论洗脱曲线[20,21]。这些结果表明，SPPs 可成功用于 SEC。

From the thermodynamic point of view, one will spread the SEC chromatogram across a greater range of retention volume

V_{R}

when the pore volume is increased. This can easily be shown by Eq (1)
从热力学角度来看，当孔隙体积增大时，SEC 色谱图将在更大的保留体积

V_{R}

范围内展开。公式 (1) 很容易说明这一点

V_{R} = V_{0} + K V_{i}

where

V_{0}

is the interstitial pore volume,

V_{i}

is the particle pore volume and

K

is the distribution constant such that

K

varies from an excluded zone

(= 0)

when the solute is larger than the pore to a fully included zone (

= 1

) when the solute is very much smaller than the pore. As the volume of internal pores

V_{i}

increases, the retention volume,

V_{R}

, will also increase. This shows that the range of separation will be increased by a larger pore volume. SPPs have less pore volume than FPPs so SPPs are at a thermodynamic disadvantage for SEC. This was thought to be a limitation of SPPs for use as SEC materials, as mentioned previously.
其中

V_{0}

是间隙孔隙体积，

V_{i}

是颗粒孔隙体积，

K

是分布常数，因此

K

会从溶质大于孔隙时的排除区

(= 0)

变化到溶质远小于孔隙时的完全包含区（

= 1

）。随着内部孔隙

V_{i}

体积的增大，截留体积

V_{R}

也会增大。这表明，孔隙体积越大，分离范围就越大。SPP 的孔体积小于 FPP，因此 SPP 在 SEC 中处于热力学劣势。如前所述，这被认为是 SPP 用作 SEC 材料的一个限制因素。

The reduced pore length, inherent in the SPP shell, has specific advantages in reducing the resistance to mass transport in the particle and faster transport kinetics provide for higher efficiency. This is also important because slow diffusional properties of large molecules that are typically separated with SEC, are compounded by the additional slowing when the solute molecular size is on the order of the pore size

[22, 23]

. Hence, the experimental determination of whether faster diffusional kinetics can overcome thermodynamic limitations is long overdue. Some of these issues were recently discussed [24] in the experimental demonstration of SEC with SPPs. In one case, SEC has been reported [25] to occur without pores.
SPP 外壳固有的孔隙长度缩短，在减少颗粒内的质量传输阻力方面具有独特的优势，而且更快的传输动力学提供了更高的效率。这一点也很重要，因为通常使用 SEC 分离的大分子的扩散特性较慢，而当溶质分子大小与孔径

[22, 23]

大小相当时，扩散特性会变得更加缓慢。因此，早就应该通过实验确定更快的扩散动力学是否能克服热力学限制。最近[24]在用 SPPs 演示 SEC 的实验中讨论了其中的一些问题。据报道[25]，在一种情况下，SEC 是在没有孔隙的情况下发生的。

In this paper we explore the use of SPP technology for SEC in the context of the interplay between particle pore volume and the efficiency of separation. It will be shown that for small and wide-pore materials that SEC with SPPs can deliver a faster separation while retaining most of the resolution of a FPP. This compromise will be suggested to be extremely important in two-dimensional separations where speed constraints often apply in the second dimension separation system. We also discuss some aspects of bioseparations pertinent to SEC using SPPs where adsorptive and partitioning mechanisms of retention exist alongside with the size-exclusion mechanism.
在本文中，我们将从粒子孔体积与分离效率之间的相互作用角度，探讨如何将 SPP 技术用于 SEC。结果表明，对于小孔和宽孔材料，使用 SPP 的 SEC 分离速度更快，同时保留了 FPP 的大部分分辨率。这种折衷方法对于二维分离极为重要，因为在二维分离系统中，速度往往受到限制。我们还讨论了与使用 SPPs 的 SEC 有关的生物分离的一些方面，其中除了尺寸排阻机制外，还存在吸附和分区保留机制。

2. Experimental and data processing conditions
2.实验和数据处理条件

2.1. Particles and columns
2.1.颗粒和柱

FPPs were obtained from the Osaka Soda Co, (Osaka, Japan). The two silica-based FPPs used in this study are SP-200-3-P and SP-1000-3 which are both of diameter

3.2 μ m

and had pore sizes nominally of

200 Å

and

1000 Å

respectively with pore volumes of

1.06 cc / g

and

0.80 cc / g

respectively, as provided by the manufacturer. SPPs, also made of silica, are from Advanced Materials Technology (Wilmington, Delaware, USA) and have nominal pore sizes of

160 Å

and

1000 Å

. These particles have outer diameters of

2.7 μ m

and

4.18 μ m

respectively and have solid core diameters of

1.7 μ m

and

3.3 μ m

respectively. These particles had pore volumes of

0.29 cc / g

and

0.20 cc / g

for the

160 Å

and

1000 Å

particles, as measured in-house using nitrogen adsorption methods. The pore size
FPP 取自大阪纯碱公司（日本大阪）。根据制造商提供的资料，本研究中使用的两种硅基 FPP 为 SP-200-3-P 和 SP-1000-3，直径均为

3.2 μ m

，孔径分别为

200 Å

和

1000 Å

，孔体积分别为

1.06 cc / g

和

0.80 cc / g

。SPP 也由二氧化硅制成，来自先进材料技术公司（美国特拉华州威尔明顿），标称孔径为

160 Å

和

1000 Å

。这些颗粒的外径分别为

2.7 μ m

和

4.18 μ m

，实心直径分别为

1.7 μ m

和

3.3 μ m

。根据内部使用氮吸附方法测量的结果，这些颗粒的孔隙体积分别为

0.29 cc / g

和

0.20 cc / g

，其中

160 Å

和

1000 Å

颗粒的孔隙体积为

0.29 cc / g

和

0.20 cc / g

。孔径
distribution of the

160 Å

SPPs was narrow and measured in-house. The

1000 Å

SPPs have a have wider distribution and this is shown in a recent paper [26]. The pore size distributions of the

200 Å

and

1000 Å

FPPs were not supplied by the manufacturer nor determined in-house. All particles of both morphologies and both pore sizes were packed into columns of dimension 4.6 mm i.d. and length 50 mm using an in-house developed proprietary packing process.

160 Å

SPP 的分布很窄，是在内部测量的。而

1000 Å

SPP 的分布范围更广，这在最近的一篇论文[26]中有所体现。

200 Å

和

1000 Å

FPP 的孔径分布既不是由制造商提供的，也不是内部测定的。两种形态和两种孔径的所有颗粒均采用内部开发的专有填料工艺填入内径 4.6 毫米、长 50 毫米的柱中。

2.2. HPLC conditions 2.2.高效液相色谱条件

Individual solutes were run at

0.25 mL / \min

and

0.50 mL / \min

flow rates at a temperature of

25^{\circ} C

using a Shimadzu Nexera

^{TM} X 2

liquid chromatograph (Shimadzu, Columbus, Maryland). The UV detector wavelength is 254 nm and the solutes were polystyrene standards of molecular weight

2.5 kDa, 5.0 kDa, 9.0 kDa, 17.5 kDa

30 kDa, 50 kDa, 110 kDa, 220 kDa, 400 kDa, 600 kDa, 900 kDa

and 1.8 mDa . The standards are from a low and high molecular weight polystyrene standards kit (Supelco, Bellefonte, PA, part numbers 4-8937 and 4-8938). The polydispersity index of these standards was not supplied by the manufacturer. The molecular weights and

\log

molecular weights are given in Table 1 along with the radius of gyration and the diameter of gyration calculated from the formula

R_{g} = 0.137 M^{0.589}

[14] for polystyrene in tetrahydrofuran (THF). THF was used for all mobile phase solvents in the unstabilized, HPLC grade form, and was from J. T. Baker (Center Valley, PA). Typically, polystyrene standards were made up as solutions in THF at

1 mg / mL

concentration with

1 μ L

injections.
使用 Shimadzu Nexera

^{TM} X 2

液相色谱仪（Shimadzu，Columbus，Maryland），在

25^{\circ} C

温度下，以

0.25 mL / \min

和

0.50 mL / \min

流速运行单个溶质。紫外检测器波长为 254 nm，溶质为分子量为

2.5 kDa, 5.0 kDa, 9.0 kDa, 17.5 kDa

、

30 kDa, 50 kDa, 110 kDa, 220 kDa, 400 kDa, 600 kDa, 900 kDa

和 1.8 mDa 的聚苯乙烯标准物质。这些标准物质来自低分子量和高分子量聚苯乙烯标准试剂盒（Supelco, Bellefonte, PA，零件编号 4-8937 和 4-8938）。制造商没有提供这些标准物质的多分散指数。表 1 列出了分子量和

\log

分子量，以及根据聚苯乙烯在四氢呋喃（THF）中的

R_{g} = 0.137 M^{0.589}

[14]公式计算出的回旋半径和回旋直径。所有流动相溶剂均使用未经稳定的 HPLC 级四氢呋喃，该溶剂来自 J. T. Baker 公司（宾夕法尼亚州，Center Valley）。通常情况下，聚苯乙烯标准物质以

1 mg / mL

浓度在 THF 中制成溶液，

1 μ L

进样。

Table 1 表 1
Radius of gyration of Polystyrene in THF.
聚苯乙烯在四氢呋喃中的回转半径。

分子量 (Da)

Molecular weight

(Da)

对数分子量

Log molecular

weight

半径回旋

(Å)

Radius of

gyration

(Å)

直径回旋

(Å)

Diameter of

gyration

(Å)

1800000

6.26

662

1325

900000

5.95

440

881

600000

5.78

347

694

400000

5.60

273

546

220000

5.34

192

384

110000

5.04

128

255

50000

4.70

160

30000

4.48

119

17500

4.24

9000

3.95

5000

3.70

2500

3.40

2.3. Data analysis 2.3.数据分析

The data, stored in Excel© spreadsheets (Microsoft, Redmond, WA), was processed for plotting using MATLABO (MathWorks, Natick, MA) version R2016a. Individual zone broadening estimates of plates and plates per unit time were obtained using the plates calculator in the Shimadzu HPLC instrument software utilizing the width at half-height method (full width at half maximum or FWHM). When interpolation is employed in the plots, the interpolation method is the cubic spline method native to MATLAB. Results were checked for spline artifacts with visual graph inspection.
数据存储在 Excel© 电子表格（Microsoft，Redmond，WA）中，使用 MATLABO（MathWorks，Natick，MA）R2016a 版本进行处理，以便绘图。使用岛津 HPLC 仪器软件中的板计算器，利用半高宽度法（半最大值全宽或 FWHM）获得了板和单位时间内板的单独区域展宽估计值。在绘图中使用插值时，插值方法是 MATLAB 原生的三次样条法。通过目测图检查结果是否存在样条假象。

It is well known that using the width at half height method can overestimate the number of plates [27-29] for peaks that are nonGaussian, typically with tailing that can be modelled with a peak model formed by the convolution of a Gaussian with an exponential tail [30]. Obtaining high accuracy plate count measurements is difficult because the peak shape is not Gaussian nor Gaussian with exponential convolution across the full molecular weight range.
众所周知，使用半高宽度法可能会高估非高斯峰的板数 [27-29]，典型的非高斯峰有尾部，可以用高斯峰与指数尾部卷积形成的峰模型来模拟 [30]。由于在整个分子量范围内，峰形既不是高斯峰形，也不是指数卷积高斯峰形，因此很难获得高精度的板数测量结果。

The specific resolution was described by Yau et al. [31,32] and originally defined as:
特定分辨率由 Yau 等人描述[31,32]，最初定义为：

R_{s p} = \frac{2 (V_{R 2} - V_{R 1})}{(W_{1} + W_{2})} \cdot \frac{1}{\log_{10} (M_{W 1} / M_{W 2})}

where

W_{1}

and

W_{2}

are the volume-based peak widths of adjacent peaks obtained by the tangent drop method. In addition,

V_{R 1}

and

V_{R 2}

are the retention volumes of adjacent peaks and

M_{W 1}

and

M_{W 2}

are the molecular weights of adjacent solute peaks.
其中，

W_{1}

和

W_{2}

是通过正切液滴法得到的相邻峰的基于体积的峰宽。此外，

V_{R 1}

和

V_{R 2}

是相邻峰的保留体积，

M_{W 1}

和

M_{W 2}

是相邻溶质峰的分子量。

In this paper we use a very similar approach. However, we use a continuous measure of the specific resolution which is constructed using interpolated time

t

, standard deviation

σ

and molecular weight

M_{w}

so that:
在本文中，我们使用了一种非常类似的方法。不过，我们使用的是一种连续的特定分辨率测量方法，该方法使用内插时间

t

、标准偏差

σ

和分子量

M_{w}

，因此：

R_{s p_{i}} = \frac{(t_{i + 1} - t_{i})}{2 (σ_{i + 1} + σ_{i})} \cdot \frac{1}{\log_{10} (M_{W i + 1} / M_{W i})}

where the 1 and 2 subscripts are replaced by the

i^{th}

and

i^{th} + 1

numbers in the interpolation vector of

t, M_{w}

and of

σ

. The standard deviation

σ

is obtained from the FWHM measurement assuming a Gaussian zone so that

σ = F W H M / 2 \sqrt{2 \ln 2}

. The specific resolution here is not normalized for comparison of columns of different lengths [31] because all of the compared columns are of the same 50 mm length.
其中，1 和 2 下标由

t, M_{w}

和

σ

的插值向量中的

i^{th}

和

i^{th} + 1

数字代替。标准偏差

σ

是根据假设为高斯区的 FWHM 测量值得出的，因此

σ = F W H M / 2 \sqrt{2 \ln 2}

。这里的具体分辨率没有为比较不同长度的色谱柱而进行归一化处理 [31]，因为所有比较的色谱柱都具有相同的 50 毫米长度。

The specific resolution

R_{sp}

is similar to other measures of separation for polymers and colloids, for example Giddings’ mass-based fractionating power [33,34] which is nearly identical to Eqs (2) and (3) and is expressed in compact form as:
比分辨率

R_{sp}

与聚合物和胶体的其他分离度量相似，例如吉丁斯的质量分馏能力 [33,34]，它与公式 (2) 和 (3) 几乎相同，并以紧凑的形式表示为：

F_{m} = \frac{R_{s}}{δ (M_{W}) / M_{W}}

where

δ

is the differential operator.
其中

δ

是微分算子。

3. Results 3.成果

3.1. Chromatograms 3.1.色谱图

The individual chromatograms of the solutes run with SPPs and FPPs are shown in Fig. 1 for all molecular weight solutes run at the flow rate of

0.25 mL / \min

. These elution curves are overlaid for specific molecular weight analytes run on

160 Å

SPP and

200 Å

FPP pore size materials (Fig. 1a and Fig. 1c respectively). The elution curves are also shown overlaid for the larger pore (

1000 Å

) SPP and FPP materials (Fig. 1b and Fig. 1d respectively). The results for both SPPs and FPPs run at

0.50 mL / \min

flow rate are not shown but look similar to that shown in Fig. 1.
图 1 显示了在

0.25 mL / \min

流速下使用 SPP 和 FPP 材料检测的所有分子量溶质的色谱图。这些洗脱曲线是在

160 Å

SPP 和

200 Å

FPP 孔径材料上运行的特定分子量分析物的叠加图（分别为图 1a 和图 1c）。图 1b 和图 1d 分别显示了较大孔径（

1000 Å

）的 SPP 和 FPP 材料的洗脱曲线。在

0.50 mL / \min

流速下运行 SPP 和 FPP 的结果没有显示，但看起来与图 1 中显示的结果类似。

One of the first things that is seen when comparing superficially porous and fully porous SEC results is that the range between the exclusion limit, where the retention volume is due to the interstitial volume only and the full pore volume, which includes the particle pore volume, is reduced for SPPs. Hence, the elution range, which is typically small in FPP SEC, is even smaller when using SPPs. This should not be surprising because the pore volume in an SPP is lower than in a FPP due to the presence of the solid core. In both particle morphologies the small pore (

160 Å

and

200 Å

pore) particles show resolution below

\approx 50 kDa

and the larger pore materials (mean pore size of

1000 Å

) show resolution of the larger solutes above

\approx 50 kDa

. As shown in Table

1, 50 kDa

corresponds to a diameter of gyration of

160 Å

, which agrees well with the pore size of the solute fractionation range. It is well known that a single pore size cannot fractionate solutes over the complete range used in these experiments

[5, 14]

.
在比较超多孔和全多孔 SEC 结果时，首先会看到的一点是，对于 SPP 而言，仅由间隙体积决定保留体积的排除极限与包括颗粒孔隙体积在内的全孔隙体积之间的范围有所缩小。因此，在 FPP SEC 中通常较小的洗脱范围，在使用 SPP 时就更小了。这并不奇怪，因为由于固体核心的存在，SPP 的孔隙体积比 FPP 小。在这两种颗粒形态中，小孔（

160 Å

和

200 Å

孔）颗粒的分辨率低于

\approx 50 kDa

，大孔材料（平均孔径为

1000 Å

）的分辨率高于

\approx 50 kDa

。如表中所示，

1, 50 kDa

对应的回转直径为

160 Å

，这与溶质分馏范围的孔径大小十分吻合。众所周知，单一孔径无法在这些实验所使用的全部范围内

[5, 14]

分馏溶质。

3.2. Retention volume range
3.2.保留体积范围

Fig. 2 shows the comparison of the retention volumes of the SPP and FPP elution results across the logarithm of the molecu-
图 2 显示了 SPP 和 FPP 洗脱结果的保留体积在分子质量的对数范围内的比较。

Fig. 1. Chromatographic elution data of polystyrene solutes and toluene superimposed on the time axis. (a) SPPs with pore size of

160 Å

, (b) SPPs with pore size of

1000 Å

, © FPPs with pore size

200 Å

(d) FPPs with pore size of

1000 Å

. All data shown here is with the flow rate of

0.25 mL / \min

.
图 1.时间轴上叠加的聚苯乙烯溶质和甲苯的色谱洗脱数据。(a) 孔径为

160 Å

的 SPPs，(b) 孔径为

1000 Å

的 SPPs，© 孔径为

200 Å

的 FPPs (d) 孔径为

1000 Å

的 FPPs。此处显示的所有数据均为流速为

0.25 mL / \min

时的数据。
lar weight range. It is seen that the retention volume range of the SPPs is less than the range of retention volumes for the FPPs. For both particle types, there is little difference in the retention volumes when comparing the two flow rate results. This suggests that for the flow rates used in this study, there is little effect of flow velocity on the distribution constant Kwhich is thermodynamic in origin. The SPP results cross at lower retention volume because the two SPP particles pack differently and the interstitial pore volume,

V_{0}

, is smaller for the

1000 Å

particle than the

160 Å

particle. For the lowest molecular weight solute, the difference in

V_{0}

also contributes to the crossing at highest retention volume, although this is
重量范围。可以看出，SPP 的保留体积范围小于 FPP 的保留体积范围。对于两种类型的颗粒，在比较两种流速的结果时，保留体积几乎没有差别。这表明，就本研究中使用的流速而言，流速对分布常数 K（热力学常数）的影响很小。SPP 结果在较低停留体积时出现交叉，这是因为两种 SPP 粒子的堆积方式不同，而且

1000 Å

粒子的间隙孔体积

V_{0}

小于

160 Å

粒子。对于分子量最低的溶质，

V_{0}

的差异也会导致最高保留体积的交叉，尽管这只是在

1000 Å

粒子上。

Fig. 2. Retention volumes of peaks across the chromatograms for the two flow rates, two pore sizes and the two different particle morphologies. The data with circles and asterisks and solid lines are for SPPs and the data with diamonds and triangles and dashed lines are for FPPs.
图 2.两种流速、两种孔径和两种不同颗粒形态下色谱图中各色谱峰的保留体积。带圆圈、星号和实线的数据为 SPPs 的数据，带菱形、三角形和虚线的数据为 FPPs 的数据。
hard to ascertain because of differences in the particle pore volume,

V_{i}

.
由于颗粒孔隙体积

V_{i}

的不同，很难确定。

As expected for the largest pore size particles, the retention volumes for both particle morphologies are similar for the largest molecules because these retention volumes should approach the exclusion limit. These retention volumes differ in the interstitial volumes of the columns. For both particle morphologies in the largest pore particles, the shape of these curves is consistent with selectivity diminishing as smaller solutes are fractionated. The selectivity reduction here is equated to the larger slope of log MW versus retention volume shown in this figure in the vicinity of the lower molecular weight solutes.
正如最大孔径颗粒所预期的那样，两种颗粒形态对最大分子的保留体积相似，因为这些保留体积应接近排除极限。这些保留体积在色谱柱的间隙体积中有所不同。对于最大孔径颗粒的两种颗粒形态，这些曲线的形状与选择性随着较小溶质的分馏而降低的情况一致。在低分子量溶质附近，选择性的降低等同于图中显示的对数截留分子量与截留体积的较大斜率。

As given in Table 1 for the largest solute of 1.8 mDa , the diameter of gyration is larger than the mean pore size of the large-pore particles and should be excluded from the pore. However, the pore size distribution of these materials is wide and therefore there is no hard cut-off into solute exclusion, besides the possibility that some of the solute can be included in the pore as the solutes are flexible random coil polymers in THF.
如表 1 所示，对于 1.8 mDa 的最大溶质，其回旋直径大于大孔颗粒的平均孔径，因此应从孔中排除。不过，这些材料的孔径分布很广，因此除了溶质在四氢呋喃中是柔性无规线圈聚合物，部分溶质有可能进入孔隙外，并没有硬性规定将溶质排除在外。

Another possibility to explain the lack of constant retention volume as the exclusion limit is approached (i.e. as the molecular size is increased beyond the pore diameter), is the presence of hydrodynamic chromatography (HDC) effects [5,35]. For larger solutes, relative to the pore diameter, the center-of-mass velocity near the outer hull of the particle surface causes faster elution as molecular size increases, which is the basis for HDC. This effect could contribute to the smaller retention volumes seen in Fig. 2 as compared to a near-vertical (constant) retention volume characteristic of pure SEC.
另一种解释在接近排阻极限时（即分子尺寸增大超过孔径时）保留体积不恒定的可能性是存在流体力学色谱（HDC）效应[5,35]。对于相对于孔径较大的溶质，随着分子尺寸的增大，颗粒表面外壁附近的质量中心速度会导致洗脱速度加快，这就是 HDC 的基础。与纯 SEC 的近乎垂直（恒定）的保留体积相比，图 2 中显示的保留体积较小，可能就是这种效应造成的。

Fig. 2 also shows that the smaller solutes are separated at higher selectivity than larger solutes with the smaller pore materials for both particle morphologies, as judged by the smaller slopes in the

\log M_{w}

versus retention volume curves at smaller molecular weights.
图 2 还显示，在两种颗粒形态下，较小的溶质比较大的溶质在较小孔隙材料中的分离选择性更高，这可以从较小分子量时

\log M_{w}

与保留体积曲线的较小斜率判断出来。

3.3. Efficiency 3.3.效率

The number of plates

N

is shown in Fig. 3a and b for the two flow rates used in this study. Immediately one can see that the
图 3a 和 b 显示了本研究中使用的两种流速下的板数

N

。可以立即看出

SPPs exhibit higher plate counts than the FPP results for both flow rates. The plate counts are generally higher at lower velocities for both particle morphologies than at higher velocities.
在两种流速下，SPP 的平板数均高于 FPP 的结果。就两种颗粒形态而言，低速时的板数通常高于高速时的板数。

One of the general trends seen in Fig. 3 is that the number of plates for excluded solutes, where larger solutes are excluded by the two smaller-pore materials independent of particle type, increases after the exclusion limit is reached. This increase is due to a decrease in zone broadening when solutes are excluded from the pore; i.e. mass transport in and out of the particle phase no longer occurs. The radius and diameter of gyration of polystyrene in THF, given in Table 1, shows that molecular weights in the vicinity of

50 kDa - 100 kDa

have diameters of gyration between

160 Å

and

200 Å

and this is the range where increased plate counts occur as shown in Fig. 3.
从图 3 中可以看出的一个总体趋势是，在达到排阻极限后，排阻溶质的板块数增加，其中较大的溶质被两种较小孔隙材料排阻，而与颗粒类型无关。这种增加是由于当溶质从孔隙中排除时，区域展宽减小；即不再发生进出颗粒相的质量传输。表 1 给出了聚苯乙烯在 THF 中的回转半径和直径，显示分子量在

50 kDa - 100 kDa

附近的回转直径在

160 Å

和

200 Å

之间，如图 3 所示，这也是板数增加的范围。

For the 1000 Å pore size particles of both morphologies, the plate numbers drop with an increase in solute molecular weight (and size). This is most likely due to the decrease in diffusion coefficient with increase in molecular weight (and size). Most of the solutes used here, except for perhaps the highest molecular weight solute, access the pore structure. The pore size distribution of most particles is rather broad for wide-pore materials and this may also explain why there appears to be access to pores with the largest solute. In the case of the

1000 Å

SPP at the higher flow rate it is noted that

σ

\approx 0.015 \min (\approx 0.9 s)

. Given

6 σ

as a baseline width this gives peaks which are 5.4 s (at baseline) wide. This is very short for SEC and shows very good performance. The contrast in efficiency with the FPP, as measured by the number of plates, suggests the potential superior use of SPPs for conducting fast separations in the SEC mode of operation.
对于两种形态的 1000 Å 孔径颗粒，平板数随着溶质分子量（和大小）的增加而下降。这很可能是由于扩散系数随着分子量（和大小）的增加而降低。除了分子量最大的溶质外，这里使用的大多数溶质都能进入孔隙结构。对于宽孔材料来说，大多数颗粒的孔径分布相当宽，这也可以解释为什么最大的溶质似乎可以进入孔隙。在流速较高的

1000 Å

SPP 的情况下，可以注意到

σ

是

\approx 0.015 \min (\approx 0.9 s)

。以

6 σ

作为基线宽度，可以得到宽度为 5.4 秒（基线）的峰值。这对于 SEC 来说是非常短的，显示出非常好的性能。与 FPP 的效率对比（以板数衡量）表明，在 SEC 运行模式下，使用 SPP 进行快速分离可能更有优势。

3.4. Rate of plate generation
3.4.平板生成率

While efficiency, as expressed in the number of plates is important, the speed of a separation is often identified with the number of plates generated per unit time [36]. This key parameter has been discussed in the context of column optimization [36,37] and is most important for SPPs as these have long been recognized as a technique which promotes faster speed operation.
以板数表示的效率固然重要，但分离速度通常是指单位时间内产生的板数[36]。这一关键参数已在色谱柱优化中进行过讨论 [36,37]，对于 SPP 而言最为重要，因为 SPP 早已被公认为是一种可加快操作速度的技术。

Fig. 3. The number of theoretical plates as a function of

\log

molecular weight for (a)

0.25 mL / \min

flow rate (b)

0.50 mL / \min

flow rate. The data with circles and asterisks and solid lines are for SPPs and the data with diamonds and triangles and dashed lines are for FPPs.
图 3.(a)

0.25 mL / \min

流速 (b)

0.50 mL / \min

流速时理论板数与

\log

分子量的函数关系。带有圆圈和星号以及实线的数据为 SPPs 的数据，带有菱形和三角形以及虚线的数据为 FPPs 的数据。

Fig. 4 a and b shows the rate of plate generation given by

N / t_{R}

as a function of the log of the solute molecular weight for the small and large pore size particles. These figures show the same pattern as in Fig. 3; SPPs for the most part generate plates at a higher rate than FPPs given approximately the same pore size, flow rate, and particle diameter. However, in this case, faster flow rates give faster rate of plate generation. The same hump of higher plate number per minute for smaller pore materials (Fig. 4a) due to solute occlusion are shown here as in Fig. 3. For the

1000 Å Å

materials at both flow rates there is seen to be a relatively constant rate of plate generation across the molecular weight range as shown in Fig. 4b.
图 4 a 和 b 显示了

N / t_{R}

所给出的小孔径和大孔径颗粒的平板生成率与溶质分子量对数的函数关系。这些数字显示了与图 3 相同的模式；在孔径、流速和颗粒直径大致相同的情况下，SPP 在大多数情况下比 FPP 产生板的速率更高。然而，在这种情况下，流速越快，板的生成速度越快。由于溶质闭塞，较小孔隙材料每分钟产生的板块数较高的驼峰（图 4a）与图 3 相同。对于

1000 Å Å

材料，在两种流速下，整个分子量范围内的平板生成速率相对恒定，如图 4b 所示。

3.5. Specific resolution 3.5.具体决议

The specific resolution is shown in Fig. 5 for the four series of experiments each at the two flow rates. As can be seen in this figure, there are two regions of maxima. For small pore materials (

160 Å

and

200 Å

) this region is at approximately

\log M_{W} \approx 4.25

and for large-pore materials (

1000 Å

) these maxima are between log

M_{W} \approx 5 - 5.5

. For both small and large pore materials, the FPPs (as annotated by dashed-lines) show higher maxima in both regions. Clearly as shown in Fig. 1, the resolution between zones in the respective molecular weight regions show higher resolution for FPPs than for SPPs. There appears to be little difference with flow
图 5 显示了在两种流速下分别进行的四个系列实验的具体分辨率。从图中可以看出，有两个最大区域。对于小孔材料（

160 Å

和

200 Å

），该区域约为

\log M_{W} \approx 4.25

；对于大孔材料（

1000 Å

），这些最大值介于对数

M_{W} \approx 5 - 5.5

之间。对于小孔和大孔材料，FPPs（如虚线所示）在这两个区域都显示出较高的最大值。显然，如图 1 所示，在各自的分子量区域中，全氟辛烷磺酸的区域分辨率高于全氟辛烷磺酸。在流动性方面似乎差别不大。

Fig. 4. Plates per unit time as a function of log molecular weight for (a) the smaller pore sizes,

160 Å

and

200 Å

(b) the wide pore size,

1000 Å

. The data with circles and asterisks and solid lines are for SPPs and the data with diamonds and triangles and dashed lines are for FPPs.
图 4.对于 (a) 较小孔径

160 Å

和

200 Å

(b) 较宽孔径

1000 Å

, 单位时间内的平板数与对数分子量的函数关系。带有圆圈和星号以及实线的数据是 SPPs 的数据，带有菱形和三角形以及虚线的数据是 FPPs 的数据。
rate with constant particle morphology and pore size, although the lowest flow rate gives highest specific resolution in all cases.
在颗粒形态和孔径不变的情况下，流速越低，比分辨率越高。

Note that specific resolution should not be interpreted as having complete resolution above the value of 1.5 , as is noted with traditional resolution. Rather these values here are biased by a molecular weight term, as shown in Eq (2) and Eq (3). However, the specific resolution can be compared between the curves shown in Fig. 5. While FPPs clearly dominate in specific resolution, in specific regions, the wide-pore SPP

1000 Å

material shows higher specific resolution up to

\log M_{W}

of 5 than the FPP material. Furthermore, the performance of the SPP material, from the viewpoint of specific resolution, shows a rather fast decline as molecular weight is increased further. It is suspected that increasing pore volume
需要注意的是，不应将比分辨率解释为在 1.5 值以上具有完全分辨率，正如传统分辨率所指出的那样。相反，如公式 (2) 和公式 (3) 所示，这些值受到分子量项的影响。不过，可以比较图 5 所示曲线的具体分辨率。虽然 FPP 在特定分辨率方面明显占优势，但在特定区域，宽孔 SPP

1000 Å

材料在

\log M_{W}

为 5 时比 FPP 材料显示出更高的特定分辨率。此外，从比分辨率的角度来看，SPP 材料的性能随着分子量的进一步增加而迅速下降。这可能与孔体积增大有关。
of the SPP may promote further specific resolution increases and overtake the

1000 Å

FPP material’s performance using this metric. The optimization of shell thickness is discussed below.
SPP 可能会促进比分辨率的进一步提高，并在这一指标上超越

1000 Å

FPP 材料的性能。下文将讨论外壳厚度的优化问题。

3.6. Peak capacity 3.6.峰值容量

The concept of peak capacity in SEC was developed by Giddings [15] for a model that assumed a constant ratio of peak width to retention time (or volume). Horváth and Lipsky contributed to this theory with a constant peak width model [38] and this was generalized by Grushka [39]. Later work by Hagel [16] assumed a variable peak width model more suitable for SEC and we will use that model here.
SEC 中峰容量的概念是由 Giddings [15] 提出的，该模型假定峰宽与保留时间（或体积）之比恒定。Horváth 和 Lipsky 提出了恒定峰宽模型[38]，并由 Grushka[39] 加以推广。后来，Hagel [16] 提出了更适合 SEC 的可变峰宽模型，我们将在此使用该模型。

Fig. 5. Specific resolution as a function of log molecular weight for the eight datasets of

0.25 mL / \min

and

0.50 mL / \min

flow rates, two pore sizes and the two different particle morphologies. The data with circles and asterisks and solid lines are for SPPs and the data with diamonds and triangles and dashed lines are for FPPs.
图 5.

0.25 mL / \min

和

0.50 mL / \min

流速、两种孔径和两种不同颗粒形态的八个数据集的比分辨率与对数分子量的函数关系。带圆圈、星号和实线的数据为 SPPs 的数据，带菱形、三角形和虚线的数据为 FPPs 的数据。

The Giddings model is approximated as
吉丁斯模型近似为

n_{c} = 1 + 0.2 \sqrt{N}

where

n_{c}

is the peak capacity. Hagel’s model for SEC [16] with a peak resolution of unity is given as:
其中

n_{c}

为峰值容量。Hagel 的 SEC 模型 [16]，峰值分辨率为统一，其计算公式为

n_{c} = 1 + \frac{(V_{p} / V_{t})}{4} \sqrt{N}

where

V_{p}

is the particle pore retention volume and

V_{t}

is the total pore retention volume (which includes the interstitial and particle pore retention volume). The plate number utilized in Eq (6) is that of a totally permeating (low molecular weight) component [16].
其中

V_{p}

是颗粒孔隙保留体积，

V_{t}

是总孔隙保留体积（包括间隙和颗粒孔隙保留体积）。公式 (6) 中使用的板数是完全渗透（低分子量）成分的板数 [16]。

The square root of the number of plates

\sqrt{N}

can be expressed as the ratio of retention time to standard deviation of a Gaussian zone

t_{r} / σ

. In Eq (6), the peak capacity is determined by the amount of particle porosity and by the ratio of a thermodynamic parameter

t_{r}

and a kinetic parameter

σ

. While the retention time is less for SPPs because of the loss of some pore volume, the extent of this loss can be compensated for smaller values in

σ

.
平板数

\sqrt{N}

的平方根可以表示为保留时间与高斯区标准偏差

t_{r} / σ

的比值。在公式 (6) 中，峰容量由颗粒孔隙率以及热力学参数

t_{r}

和动力学参数

σ

的比值决定。虽然 SPP 的保留时间会因为一些孔隙体积的损失而缩短，但这种损失的程度可以通过

σ

的较小值来补偿。

The values of

t_{r} / σ

for FPPs and SPPs are compared in Table 2 for the totally permeating peak where it is shown that the SPPs at approximately equal pore size have larger

t_{r} / σ

values. Also included in Table 2 is the ratio of

V_{p} / V_{t}

and the calculation of

n_{c}

. The values of

V_{t}

are obtained from the toluene void retention volume and

V_{p}

is obtained by the difference in retention volumes between toluene and the 900 kDa solute which should be near the exclusion limit. The exclusion limit is not particularly distinct for both SPP and FPP experiments, as viewed by the results in Fig. 2. This may be due to solute adsorption, partial exclusion, HDC effects or a combination of these effects.
表 2 比较了完全渗透峰的 FPP 和 SPP 的

t_{r} / σ

值，结果表明，孔径大致相同的 SPP 具有较大的

t_{r} / σ

值。表 2 还包括

V_{p} / V_{t}

的比率和

n_{c}

的计算结果。

V_{t}

的值由甲苯空隙保留体积得出，

V_{p}

的值由甲苯和 900 kDa 溶质的保留体积差值得出，该值应接近排除极限。从图 2 中的结果来看，SPP 和 FPP 实验的排阻极限并不特别明显。这可能是由于溶质吸附、部分排阻、HDC 效应或这些效应的综合作用造成的。

The comparison of peak capacity values of the smaller pore size particles favors the FPP morphology. However, it is shown that the wide pore particles have very similar peak capacities. Clearly the ratio

V_{p} / V_{t}

favors FPPs as the core-shell morphology has less volume in the shell than a FPP. The diffusion length is much shorter in the superficially porous material and the peaks are narrower which would tend to preserve the peak capacity of the separation system
通过比较较小孔径颗粒的峰值容量值，可以看出 FPP 形态更受青睐。不过，宽孔径颗粒的峰值容量非常相似。很明显，

V_{p} / V_{t}

比更倾向于 FPP，因为核壳形态比 FPP 的壳体积更小。表层多孔材料的扩散长度更短，峰值更窄，这将有利于保持分离系统的峰值容量。
and make the limited elution range faster for SPPs. With a somewhat larger shell thickness, the peak capacity could probably be made to favor the SPP for a smaller pore particle.
并使 SPP 在有限的洗脱范围内更快。如果外壳厚度稍大一些，那么对于孔隙较小的颗粒来说，峰容量可能会更有利于 SPP。

4. Discussion 4.讨论

Due to sampling considerations [40,41] it is often necessary to run a fast second dimension separator in two-dimensional liquid chromatography (2DLC) so that the first dimension peak can be adequately sampled by the second dimension separator [42]. Proper sampling aids quantitation, peak detection algorithms, and helps prevent ionization suppression when mass spectrometry is used as a detector [43]. In many applications of 2DLC [40,44-46] SEC has been utilized as the second dimension separation column. In these cases, SEC with SPPs could enhance the application by allowing for faster operation and/or more sampling. SEC in the second dimension is also useful as a desalting step prior to mass spectrometry.
由于取样方面的考虑 [40,41]，通常需要在二维液相色谱（2DLC）中运行快速的二维分离器，以便二维分离器对一维峰进行充分取样 [42]。适当的取样有助于定量和峰值检测算法，并在使用质谱作为检测器时有助于防止电离抑制[43]。在 2DLC 的许多应用中 [40,44-46]，SEC 被用作二维分离柱。在这些情况下，使用 SPP 的 SEC 可以加快操作速度和/或增加采样次数，从而提高应用效果。二维 SEC 还可用作质谱分析前的脱盐步骤。

The choice of pore size is an often critical choice for SEC. Column coupling, in which two columns of different pore sizes are used in series to expand the separation range

[5, 14]

is well known. The results shown in this paper used two different pore sizes for the whole range of molecular weight solute standards and these pore sizes are not optimized for performance. The optimization of the pore size and choice of shell thickness for SEC with SPPs is not a trivial matter [47]. This is because increasing the shell thickness gives more pore volume at a reduction in column efficiency. However, that balance is very dependent on the solute size and the pore size. This may result in the situation where maximizing speed and/or resolution of separation will depend both on the pore size and shell thickness across the molecular weight range.
孔径的选择往往是 SEC 的关键选择。众所周知，色谱柱联用是指将两个不同孔径的色谱柱串联使用，以扩大分离范围

[5, 14]

。本文所显示的结果是在整个分子量溶质标准范围内使用了两种不同的孔径，而这些孔径并没有经过性能优化。对于使用 SPP 的 SEC 来说，孔径的优化和外壳厚度的选择并非易事 [47]。这是因为增加外壳厚度会增加孔隙体积，但会降低色谱柱效率。然而，这种平衡在很大程度上取决于溶质大小和孔径大小。这可能会导致在整个分子量范围内，分离速度和/或分辨率的最大化同时取决于孔径和外壳厚度。

A further aspect of this optimization is that for many biomolecules of substantial molecular weight (and size), the traditional retention mechanism and subsequent elution is controlled by the solvent gradient. This is exemplified in reversed phase, normal phase and ion exchange chromatography where enthalpy-driven retention results in almost infinite retention until a critical composition of the gradient is reached. As retention is reduced at or
这种优化的另一个方面是，对于许多分子量（和大小）很大的生物大分子来说，传统的保留机制和随后的洗脱是由溶剂梯度控制的。这在反相、正相和离子交换色谱中均有体现，在达到梯度的临界成分之前，焓驱动的保留几乎是无限的。在或

Table 2 表 2
The values used in calculating peak capacity for the SPP and FPP results. The units of the pore volumes

V_{P}

and

V_{t}

is mL .
用于计算 SPP 和 FPP 结果峰值容量的数值。孔隙体积

V_{P}

和

V_{t}

的单位是 mL。

Morphology 形态学	Pore size (A) 孔径 (A)	flow rate ( $mL / \min$ ) 流量 ( $mL / \min$ )	$V_{p}$	$V_{t}$	$V_{p} / V_{t}$	N	$\sqrt{N = t / σ}$	$n_{c}$
SPP	160	0.25	0.164	0.544	0.301	4907	70.0	6.3
SPP	160	0.5	0.164	0.542	0.303	7056	84.0	7.4
SPP	1000	0.25	0.176	0.497	0.354	3410	58.4	6.2
SPP	1000	0.5	0.176	0.497	0.354	5399	73.5	7.5
FPP	200	0.25	0.379	0.666	0.569	2658	51.6	8.3
FPP	200	0.5	0.376	0.663	0.567	3731	61.1	9.7
FPP	1000	0.25	0.303	0.675	0.448	2717	52.1	6.8
FPP	1000	0.5	0.299	0.675	0.443	3926	62.7	7.9

near the critical gradient composition, SPPs have been shown to offer substantial performance advantages in speed and efficiency for larger biomolecules [48-50]. This is attributed to the mass transport advantages of having thin shells and shorter diffusion distances.
在临界梯度成分附近，SPPs 已被证明在较大生物分子的速度和效率方面具有很大的性能优势 [48-50]。这归因于具有薄壳和较短扩散距离的质量传输优势。

It is possible that selectivity is then enhanced with sizeexclusion processes aiding the separation as enthalpic retention approaches near zero during gradient elution and the SEC mechanism becomes more important when the solute size is some fraction of the average pore size.
在梯度洗脱过程中，当焓滞留接近零时，尺寸排阻过程会帮助分离，从而提高选择性；当溶质尺寸是平均孔径的一部分时，SEC 机制就变得更加重要。

This mechanism appears even more complex as mass transport studies of model wide-pore materials has shown that wide-pore SPPs have perfusive (diffusion aided by convection) flow in a substantial region of the porous shell with

10 %

of the mass flux in the particle bed being in the shell region [51]. This can facilitate faster mass transport for even more efficiency [52-54].
对模型宽孔材料进行的质量传输研究表明，宽孔 SPP 在多孔壳的大部分区域都有灌注流（对流辅助扩散），颗粒床中的质量通量

10 %

都在壳区，因此这种机制显得更加复杂[51]。这有助于加快质量传输速度，提高效率[52-54]。

With SPPs on the order of

\geq 2 μ m

particle diameters, the pressure drop is not excessive and this aids in using longer columns (and columns in series), a common practice in SEC [5,14]. Both SPP and FPP particles can be used in longer columns to increase resolution. When time is not critical, the FPPs are expected to outperform SPPs with respect to specific resolution. If speed is important, SPPs can perform faster separations in the allotted time.
SPP 的颗粒直径在

\geq 2 μ m

数量级，压降不会过大，这有助于使用较长的色谱柱（和串联色谱柱），这在 SEC 中是常见的做法 [5,14]。SPP 和 FPP 颗粒都可用于较长的色谱柱，以提高分辨率。当时间不是关键因素时，FPP 在具体分辨率方面有望优于 SPP。如果速度很重要，则 SPP 可在规定时间内进行更快的分离。

It has been established that chromatographic elution of small molecules in SPPs is affected by both the B term and C terms of the van Deemter equation [55-57]. Both terms, for small molecule separations, appear smaller for SPPs as compared with FPPs [55,56]. For larger molecules, as are typically fractionated with SEC, both terms will be affected by the inherently smaller diffusion coefficient of larger molecules. Further details of the theoretical development of SEC with SPPs is forthcoming [47] along with plate height data for this application.
已经证实，小分子在 SPPs 中的色谱洗脱受到 van Deemter 方程中 B 项和 C 项的影响 [55-57]。对于小分子分离而言，SPP 的这两个项均小于 FPP [55,56]。对于较大的分子（通常用 SEC 分离），这两个项都会受到较大分子固有的较小扩散系数的影响。有关使用 SPPs 的 SEC 理论发展的更多详情以及该应用的板高数据即将公布 [47]。

As we have shown in this paper, SPPs may have some very useful properties in the SEC mode. Future optimization of particle morphology and applications which clearly show the speed of SEC with SPPs will further demonstrate potential advantages of this technology.
正如我们在本文中所展示的，SPP 在 SEC 模式下可能具有一些非常有用的特性。未来对粒子形态的优化，以及明确显示使用 SPPs 的 SEC 速度的应用，将进一步证明这种技术的潜在优势。

Acknowledgement 鸣谢

The support of the National Institutes of Health under grant R44-GM108122-02 is gratefully acknowledged as are discussions with Tim Langlois and Stephanie Schuster of Advanced Materials Technology, Inc.
感谢美国国立卫生研究院 R44-GM108122-02 号基金的支持，以及与先进材料技术公司 Tim Langlois 和 Stephanie Schuster 的讨论。

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- Corresponding author. 通讯作者：
E-mail address: Mark.Schure@GMail.com (M.R. Schure).
电子邮件地址：Mark.Schure@GMail.com (M.R. Schure)。

Size exclusion chromatography with superficially porous particles 超微孔颗粒尺寸排除色谱法

A R T IC LE IN F O在 F O

Article history: 文章历史：

Keywords: 关键词：

Abstract 摘要

1. Introduction 1.导言

2. Experimental and data processing conditions2.实验和数据处理条件

2.1. Particles and columns2.1.颗粒和柱

2.2. HPLC conditions 2.2.高效液相色谱条件

2.3. Data analysis 2.3.数据分析

3. Results 3.成果

3.1. Chromatograms 3.1.色谱图

3.2. Retention volume range3.2.保留体积范围

3.3. Efficiency 3.3.效率

3.4. Rate of plate generation3.4.平板生成率

3.5. Specific resolution 3.5.具体决议

3.6. Peak capacity 3.6.峰值容量

4. Discussion 4.讨论

Acknowledgement 鸣谢

References 参考资料

Size exclusion chromatography with superficially porous particles
超微孔颗粒尺寸排除色谱法

A R T IC LE IN F O
在 F O

2. Experimental and data processing conditions
2.实验和数据处理条件

2.1. Particles and columns
2.1.颗粒和柱

3.2. Retention volume range
3.2.保留体积范围

3.4. Rate of plate generation
3.4.平板生成率