Can GPC/SEC determine if my sample is branched?

by Kyle Williams, Thursday, 15th November 2018

GPC/SEC 能否确定我的样品是否有分支？

While talking to customers about their samples, a frequent topic that comes up is whether or not their samples are branched.  Fortunately, I work primarily with Malvern Panalytical’s gel permeation / size exclusion chromatography (GPC/SEC) product range, which in addition to providing molecular weight, intrinsic viscosity (IV), and hydrodynamic radius (Rh) data, offers the ideal technique to observe, and even quantify, the extent of branching within a sample.  In this post, I’m going to describe what it means for a sample to be branched, how branching affects a sample’s molecular structure, and how GPC/SEC can be used to measure branching.

在与客户讨论他们的样品时，一个经常出现的话题是他们的样品是否有分支。幸运的是，我主要使用 Malvern Panalytical 的凝胶渗透/体积排阻色谱(GPC/SEC) 产品系列，该技术除了提供分子量、特性粘度（IV）和流体动力学半径（Rh）数据外，还提供观察甚至量化样品内分支程度的理想技术。在本文中，我将描述样品有分支意味着什么，分支如何影响样品的分子结构，以及如何使用 GPC/SEC 测量分支。

Let’s begin by defining what it means for a sample to be branched or to exhibit branching. A branch point in a polymer is a trifunctional (or greater) point where a secondary chain has propagated from the primary, linear backbone of the molecule. From a practical standpoint, this means that on a material level the polymer chains within a sample are unable to pack as tightly, which often results in stretchy or flexible end-use materials. Some materials are designed to be consistently branched (think of the molecule shaped like a comb), some randomly branched, while others end up branched as an unintentional result of the polymerization event. Whether intentional or not, observing and potentially quantifying branching within a sample is a key part of complete characterization.

首先定义样品有分支或表现出分支的含义。聚合物中的分支点是三功能（或更多）点，在此点上，次链从分子的主线性主链传播。从实践角度来说，这意味着在材料层面，样品内的聚合物链无法紧密地堆积，这通常导致成品材料具有可拉伸性或柔韧性。有些材料被设计成持续分支（可以想到像梳子形状的分子），有些则是随机分支，而另一些则因为聚合事件的意外结果而形成分支。无论是否为刻意设计，观察并有可能量化样品中的分支都是完整表征的重要组成部分。

In addition to making it difficult for polymer chains to pack together, branching affects the structure of a single polymer chain by making it more dense. This may be counterintuitive considering that branching typically results in the final product being more flexible, or less dense, but on a molecular level a branch point increases the amount of mass in a given volume, thus increasing the molecular density.

除了使聚合物链难以聚集在一起，分支还通过使单个聚合物链变得更密集来影响其结构。这可能与直觉相反，因为分支通常使最终产品更具灵活性或密度更低，但在分子水平上，分支点增加了给定体积内的质量量，从而增加了分子密度。

The figure below depicts two polymer chains with equal mass, one linear and one branched. The volume occupied by the branched chain is less than that of the linear chain, resulting in a higher molecular density for the branched chain. This difference in molecular density between a linear and branched sample is what allows branching to be observed.

下图显示了两个质量相等的聚合物链，一个是线性的，一个是分支的。分支链占据的体积小于线性链，从而导致分支链的分子密度更高。这种线性和分支样本之间的分子密度差异使得能够观察到分支。

As indicated by the bottom line in the above figure, the difference in molecular density generated from branching manifests itself as a difference in measured IV. The units of IV are dL/g, or volume per mass, and represents an inverse density figure. This inverse relationship is why the molecular density increases with branching, whereas the IV decreases. Needless to say, the presence of a viscometer detector in a GPC/SEC system is critical for observing and characterizing branching within samples.

如上图底线所示，由分支产生的分子密度差异表现为测量的 IV 差异。IV 的单位是 dL/g，即每单位质量的体积，代表了一种反密度数值。这种反向关系解释了为什么分子密度随着分支增加，而 IV 减小。不过多说，GPC/SEC 系统中存在粘度计检测器对于观察和表征样品中的分支至关重要。

The best way to study a sample’s molecular structure is through the Mark-Houwink (MH) plot, which plots a sample’s IV on the y-axis against its molecular weight on the x-axis. Polymers with consistent structures throughout their molecular weight range have MH plots that appear as straight lines, as their molecular size, and thus IV, increases at a consistent rate with increasing molecular weight. Samples with similar structures will have MH plots that overlay or exist along the same line. Samples with different molecular densities will appear “stacked,” with the densest material situated lowest in the plot.

研究样品分子结构的最佳方法是通过 Mark-Houwink (MH) 图，其将样品的 IV 作为 y 轴，与其分子量在 x 轴上绘制。分子量范围内结构一致的聚合物其 MH 图像直线，因为其分子尺寸，进而 IV，随着分子量的增加以一致的速率增加。结构相似的样品将拥有重叠或位于同一条线上的 MH 图。分子密度不同的样品将显示“堆叠”效果，其中密度最大的材料位于图的最下方。

If a material is branched, its MH plot will appear to curve downward with increasing molecular weight, as compared to a linear analogue.  This is illustrated in the figure below, where the red and purple lines represent a linear sample and the curved lines represent a variety of branched samples.

如果材料有分支，与线性类似物相比，其 MH 图将随着分子量的增加而向下弯曲。下图中直线为红色和紫色，代表线性样品，曲线表示各种分支样品。

The reason branched samples appear curved is because of the branch points, which increase the molecular density.  Since molecular density and intrinsic viscosity are inversely related, when the molecular density increases at a given molecular weight, the intrinsic viscosity decreases.  As the plot moves along the x-axis to the right, the molecular weight of the sample increases, which means there are more opportunities for branch points, and so the differences between linear and branched samples grows with increasing molecular weight.  This difference between the plots for the linear and branched samples provides the basis for branching calculations.

分支样品呈现弯曲形状的原因是由于分支点增加了分子密度。由于分子密度和特性粘度呈反比，当分子密度在给定分子量下增加时，特性粘度减小。当图在 x 轴上向右移动时，样品分子量增加，这意味着有更多的分支点，因此线性样品和分支样品之间的差异随着分子量的增加而变大。这种线性和分支样品图之间的差异为分支计算提供了基础。

These plots show examples of long-chain branching, in which the branching increases along with molecular weight.  A Mark-Houwink plot of a sample exhibiting short-chain branching, where the molecule possesses regular, short branches consistently present throughout its structure, would look more like the stacked plots described above.  An example of this would be the differences between polyethylene and polypropylene, shown below, in which both samples have an identical saturated hydrocarbon backbone, but the polypropylene sample has a methyl substituent on every other carbon.  In this case the molecular density of polypropylene is greater than that of polyethylene, but the amount of branching does not increase with molecular weight, as the length of each branch remains the same regardless of molecular weight.  The differences between polyethylene and polypropylene are typically described as arising from differences in molecular structure, not due to branching.

这些图展示了长链分支的例子，其中分支随着分子量的增加而增加。一种表现为短链分支的样品的 Mark-Houwink 图，其中分子具有一致存在于其结构中的规则短分支，看起来更像上面描述的堆叠图。这种情况的一个例子是聚乙烯和聚丙烯的差异，见下图中，在这种情况下，两个样品都有相同的饱和碳氢化合物骨架，但聚丙烯样品在每隔一个碳上有一个甲基取代基。在这种情况下，聚丙烯的分子密度大于聚乙烯，但分支量不会随着分子量增加而增加，因为每个分支的长度保持不变。聚乙烯和聚丙烯之间的差异通常描述为因分子结构的差异引起的，不是由于分支。

Malvern Panalytical’s OmniSEC software is designed to calculate long chain branching using the three most common Zimm-Stockmayer equations for branching.  These models compare the IV of a linear reference and branched sample at each molecular weight.  If a linear reference, such as the black plot in the figure below, is not available, then the user can generate one by entering the appropriate MH parameters a and log K or by using the lower molecular weight, linear region of a sample’s MH plot to approximate its trajectory.

Malvern Panalytical 的 OmniSEC 软件用于使用三种最常见的 Zimm-Stockmayer 分支方程计算长链分支。这些模型在每个分子量上比较线性参考和分支样本的 IV。如果没有线性参考，例如下图中的黑色曲线，用户可以通过输入适当的 MH 参数 a 和 log K，或者通过使用样品 MH 图的较低分子量线性区域来生成一条近似轨迹。

A video demonstration of the branching analysis method, including demo data with which you can practice, can be found by clicking here and on the image below. Calculated data available from this type of analysis includes branching number (Bn), or average number of branches per chain, and branching frequency (λ). These pieces of data, along with the MH parameters a and log K, provide detailed insight into the molecular structure of a sample. The best part is that all of this data can be obtained from a single injection of a sample on a multidetector GPC/SEC instrument!

包括可以供您练习的示范数据在内的分支分析方法视频演示，可以通过单击此处和下图找到。此类分析可用的计算数据包括分支数（Bn），即每链的平均分支数，以及分支频率（λ）。这些数据与 MH 参数 a 和 log K 一起，为样品的分子结构提供详细见解。最重要的是，所有这些数据都可以通过在多检测器 GPC/SEC 仪器上对样品进行单次注射获得！

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